Quantitative Methods in Finance
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FIN617-chapter11CFQ20201.pptxQuantitative Methods in Finance
FIN 617
Professor Edwalds
Chapter 11 Topic 5
Review Questions
What is the Carhart-Fama-French model?
Answer:
The Carhart-Fama-French model is a multifactor extension of CAPM that describes the returns on stocks in terms of their sensitivity to market risk plus extra return for small cap stocks, value stocks (with high book-to-market ratios), and momentum stocks (the ones with the highest returns over the past year)
The equation is:
Review Questions
What do the factors in a macroeconomic multifactor model measure?
Answer: The factors in a macroeconomic multifactor model measure the difference between actual and anticipated values, or the “surprise”, in macroeconomic indicators such as GDP growth, unemployment, inflation, interest rates, and credit spreads
Review Questions
What are standardized betas in fundamental multifactor models?
Answer:
In fundamental multifactor models, standardized betas are characteristics of the stock measured by the number of standard deviations between the value of the attribute for this stock and the mean of the attribute for all stocks.
For attributes measured on a nominal scale, the standardized beta is 1 if the stock has the attribute or 0 if it does not.
Applications: Return Attribution
Active return
Excess of portfolio return over benchmark portfolio return
Two components:
Factor tilt
Security selection
Factor tilt
Excess of portfolio sensitivity over benchmark for each risk factor
Times actual return for that factor
Security Selection
Remainder of active return
Return Attribution Example
Return Attribution Observations
Benchmark is index of 1000 largest US stocks by market value
Tilts toward large cap, so negative sensitivity to small cap (SMB)
Return was 9.16% more than risk-free rate
Selected portfolio similar to benchmark in risk profile
Tilted toward value stocks (positive HML exposure)
Slight tilt toward large cap with lower market risk
Selected portfolio beat benchmark by 2.0741%
Value stocks tilt gives 98.4% of this excess return
Tilt away from market risk lost return of 0.276%
Stock selection lost return of 0.05%
Applications: Risk Attribution
Active Risk
Tracking Error
Information Ratio
Active Risk Squared
Variance of active return
Active factor risk + Active specific risk
Active specific risk
Where
And is residual risk from the factor model regression for stock i
Active factor risk found indirectly
Portion of ARS due to factor tilts
Risk Decomposition Example
Risk Decomposition Example (continued)
Risk Decomposition Observations
Portfolio A has largest active risk exposure
Proportion of active factor risk and active specific risk similar between portfolios A and B
Portfolio A has substantial industry risk exposure
Portfolio B has similar industry risk exposure as benchmark
Portfolio B has higher exposure to style (size, liquidity, leverage, dividend, etc)
Portfolios B an C have similar overall active risk
Portfolio C has higher exposure to style, less to specific stocks
Portfolio D appears to be passively managed, tracking benchmark
Portfolio Construction
Passive management
Track index by mirroring exposure to factors
Active management
Establish desired risk/return profile using multifactor model
Predict alpha (excess risk-adjusted returns)
Rules-based active management (alternative indexes)
Tilt portfolio toward specific factors vs standard indexes (market cap based)
Low cost, transparent approach
Intentional factor and style biases
Homework
Workbook Chapter 11 problems:
#4, #5, and #6
Complete Chapter 11 homework assignment:
#1, #2, #3, #4, #5, and #6
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